Finite Group Databasebeta

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AGL(1,𝔽5)×#64241 #72269764

order5760
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productAGL(1,𝔽5)×#64241

Splittings

FittingC22×C32×C5 ⋊ C4×D4
HallC32×C5 ⋊ C4×#120
SylowC32 ⋊ AGL(1,𝔽5)×#120
SylowC5 ⋊ C4×#64241

Subgroups

subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽5)×GO+(4,𝔽2)
commutatorC2×C5×C3⋊D3C23×C4
FittingC22×C32×C5C4×D4
socleC2×C32×C5C2×C4×D4
prime radicalD5×#64241C2
cosocleC2×D5×C3⋊D3C24
hypercenterC22AGL(1,𝔽5)×GO+(4,𝔽2)
hypocenterC32×C5C4×#120
LCSG ▷ C2×C5×C3⋊D3 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

4236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 60

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.